Modeling EPR Powder Spectra Using Numerical Diagonalization of the Spin Hamiltonian

Abstract

A new modeling code, ZFSFIT (standing for Zero Field Splitting FITting), written in FORTRAN 77 is proposed. It is designed for computing and fitting EPR powder spectra described by any spin Hamiltonian including second- and fourth-order ZFS terms (S ≤52) and/or a hyperfine term (I ≤72). Based on numerical diagonalization of the spin Hamiltonian, this code computes the powder spectrum, the calculated angular dependencies, and the energy levels at any orientation. Least-squares refinement of the spin Hamiltonian parameters is performed either by adjusting powder line positions (EPRPLP module) or by directly fitting the powder spectra (ZFSFIT code). Especially, simultaneous fitting of EPR powder line positions recorded at distinct frequencies improves the accuracy of the refined EPR parameters. Superhyperfine effects as well as broadening effects due to site-to-site distribution of g-, A-, and ZFS parameters are treated using first-order perturbation theory and can also be refined. Parameters for several distinct centers can be fitted simultaneously, allowing quantification of their relative amounts in the sample. After a description of the algorithm, determination of second- and fourth-order ZFS parameters of Cr3+, Mn2+, and Fe3+centers in low-symmetry sites in minerals are treated, including first evidence of structural Fe3+centers in αAl(OH)3. The code is available without charge to academic users from the authors.